My daughter is a little over 3 months old. I am scared that she may have autism. My sister has it, so maybe I am just paranoid. My daughter is sometimes scared of strangers or people she hasn't seen in awhile. She will usually smile at others, but will often cry when they hold her. She seems to be really scared of them. She is usually fine when my husband or I hold her.
She often stares at ceiling fans, too. She also doesn't usually like to be held in the cradle position. She will often arch her back and put her head back like she hates it. I read somewhere that this is a sign of a developmental delay.
She does smile often, and loves to look at faces. She laughs when tickled, and she is already rolling over from her back to her stomach. She also reaches for objects, and puts them in her mouth.
Should I be worried?
No, you should not be worried given what you have written about your daughter. To meet the definition of autism (or PDD) there must be impaired social skills, language skills, and unusual motor activities (like repeating behaviors over and over or fixating on a narrow range of objects).
Taking these one by one: smiling at faces, laughing and the enjoyment of human interaction are all normal and reassuring social skills in your daughter. The balking at being given over to others is the beginning of normal stranger anxiety.
You didn't specifically mention language skills, but she should be making lots of wet, messy vowels in response to your attention, and calming down with your soothing voice.
Her motor skills should include reaching and mouthing objects, just as you describe. The arching with a position she doesn't like in itself doesn't mean much. Staring at an interesting object like a ceiling fan is in no way worrisome.
Can anyone give you 100 percent assurance that autistic symptoms won't ever develop? No, but you are describing today very normal 3 to 4-month-old behavior.